Conversion of a plan into a viable cognitive vehicle

Adhering to God's Plan in a Global Society (Part #8)

The two-dimensionality of a plan, as explored above, may be employed metaphorically to highlight the contrast between such a surface (or platform) and the design of a cognitive vehicle through which the noosphere might be navigated. An imaginative point of departure is the existence of a mythical magic carpet as a form of vehicle -- a form of divine plan offering personal mobility.

Exploiting "threads" as required for carpet weaving and, metaphorically, in (internet) conversation threading, the challenge is how to interweave threads of relevance such as to configure a vehicle, as separately discussed (Interweaving Thematic Threads and Learning Pathways: Noonautics, Magic carpets and Wizdomes, 2009). Such interweaving can be considered in systemic terms (Magic Carpets as Psychoactive System Diagrams, 2010). There is some irony in use of the carpet metaphor in that the 15 transformations (mentioned above in relation to the Millennium Project's 15 strategic challenges) were partially inspired by Christopher Alexander's analysis of traditional carpet design (A Foreshadowing of 21st Century Art: the color and geometry of very early Turkish carpets, 1993).

The various "numbers" by which globality may be ordered and become apparent -- most notably in the light of the perceptial challenges of the magical number 7 plus or minus 2 -- suggest that closure on any particular pattern may be premature at this time. This is especially the case with respect to the belief systems of the world, as mentioned above in the light of the argument of Stephen Prothero (God Is Not One: the eight rival religions that run the world -- and why their differences matter, 2011). His indication of a "ninth" is then particularly relevant.

Whether with respect to Alexander's 15 transformations, or the set of 15 global strategic challenges, is the emergent "magic" of globality to be understood as associated with the human cognitive engagement with so-called magic squares, as discussed separately (Patterns Essential to Individual and Global Health? 2010). How might this relate to appreciation of the symmetry of the icosahedron with its 15 great circles (depicted above)? The issue is highlighted by the following:

Emergent perception of globality through a magic square?
columns, rows and diagonals all total to 15
(reproduced from Wikipedia)

The warp and weft of woven carpets also recall the reference above to spreadsheet organization (Warp and Weft of Future Governance: ninefold interweaving of incommensurable threads of discourse, 2010). The geometrical or topological) transformation of the planar spreadsheet into some form of container can be usefully explored through the transformation of a matrix into a torus, as separately discussed (Comprehension of Requisite Variety for Sustainable Psychosocial Dynamics: transforming a matrix classification onto intertwined tori, 2006).

The projection of a matrix (spreadsheet) onto a torus can be achieved in two distinct ways (which are of course topologically equivalent):

Mode A: by curving the matrix so that the top row and the bottom row are contiguous -- thus forming a cylinder. The cylinder is then curved so that the two circular ends meet. The leftmost column is then contiguous with the rightmost column.
Mode B: by curving the matrix so that the leftmost column and the rightmost are contiguous -- thus forming a cylinder. The cylinder is then curved so that the two circular ends meet. The top row is then contiguous with the bottom row.

Transition from matrix to torus

plan	conduit	container

In contrast with either plane or cylinder, the torus is potentially a "viable container" -- as might be expected of what is implied by either God's Plan or some secular equivalent. As a container, the torus offers a particular sense of "comprehension", with its implication of being self-reinforcing in a mnemonic sense -- as a consequence of "wrapping" around.

Speculations regarding the shape of the universe are then of relevance -- whether as the domain of God or of secular understanding. These speculations are of course framed in astrophysical terms, although these may well have cognitive, psychosocial analogues with respect to the noosphere or the universe of knowledge.

The design of a cognitive vehicle is discussed and illustrated separately with respect to its embodiment (Embodying a navigable cognitive vehicle, 2014; Organizing, starting and driving a cognitive vehicle, 2014). With respect to any sense of its operation -- namely the operation of any plan in practice -- of particular interest is how the circular reconfiguration of the spreadsheet depiction then implies a pattern of interlocking feedback loops in cybernetic terms, as addressed by Maurice Yolles (Organisations as Complex Systems: an introduction to knowledge cybernetics, 2006). Organization in terms of plan, conduit or container might then be explored in terms of first-, second- and third-order cybernetics as clarified by Yolles. The relevance of a fourth-order, to which he refers, might then be associated with the above-mentioned intertwining of tori (Comprehension of Requisite Variety for Sustainable Psychosocial Dynamics, 2006). It is the double curvature (even triple or more) with which a sense of coherence, credibility and memorability are especially associated.

The speculations of astrophysics are concerned with the geometry and the topology of the whole universe, whether observable or otherwise. While the local geometry does not determine the global geometry completely, it does limit the possibilities, particularly a geometry of a constant curvature. Investigations with regard to global structure currently consider:

whether the universe is infinite or finite in extent
the scale or size of the entire universe (if it is finite)
whether the geometry is flat, positively curved, or negatively curved
whether the topology is simply connected like a sphere or multiply connected like a torus

It is appropriate to consider whether and how such issues should inform understanding of the integrative divinity from which God's Plan purportedly emanates or the coherence of the globality with which any secular global plan might be expected to be consistent. The following images from Wikipedia are fruitful guides to such reflection.

As shown in the left-hand image below, the local geometry of the universe is determined by whether the density parameter O is greater than, less than, or equal to 1: From top to bottom: a spherical universe with O > 1, a hyperbolic universe with O < 1, and a flat universe with O = 1. Note that these depictions of two-dimensional surfaces are merely easily visualizable analogues to the 3-dimensional structure of (local) space.

Geometry of the universe Global versus Local (reproduced from Wikipedia)	Animation indicative of topological relation between torus and sphere (reproduced from Wikipedia)

The animation on the right above is usefully indicative of how any sense of globality might be embedded dynamically within a more complex topology. Whilst the sphere is a common symbol of globality and some understandings of divinity, it is appropriate to note that the torus has been envisaged as a viable design for extraterrestrial habitats for space colonies, but has also long been associated with an understanding of spirituality and holiness in the form of a halo.

These images offer interrelated forms of relevance to any discussion regarding the limitless resources cited by some as available to humanity (as implied by an infinite plane) -- in relation to understandings of how such resources might be constrained within a global society, or by any sense of global comprehension.

Imaginative reflection relevant to this argument can be taken further through consideration of the topology of:

the Klein bottle and its particular relation to the torus (Intercourse with Globality through Enacting a Klein bottle: cognitive implication in a polysensorial "lens", 2009). This is notably a preoccupation of Steven M. Rosen (Topologies of the Flesh: a multidimensional exploration of the lifeworld, 2006; Dimensions of Apeiron: a topological phenomenology of space, time, and individuation, 2004).
sphere eversion, namely how a sphere can be turned "inside out" in the light of Smale's paradox (Sphere eversion as guide to the cognitive twist of global introversion? 2013; World Introversion through Paracycling: global potential for living sustainably "outside-inside", 2013).
the drilled truncated cube (a Stewart toroid), namely a toroidal polyhedron but with 64 edges (of 9 types). This is of particular value as a unique means of holding the set of 64 I Ching hexagrams -- understood as encoding all conditions of change, as separately illustrated (Enabling Wisdom Dynamically within Intertwined Tori: requisite resonance in global knowledge architecture, 2012). This offers an unusually articulated "global" configuration. The form might also be used as a means of mapping the 62 possible views concerning the nature of self in relation to the world, articulated in the Buddhist text entitled the Brahmajala Sutta (The Discourse on the All-Embracing Net of Views), as discussed separately (Comprehensive set of ways of knowing, 2009). In this sense individual "views" are fruitfully related to the sense of "plan" -- but configured globally through such a mapping.
the curious form of the Szilassi polyhedron (also a Stewart toroid) is potentially of great interest as another means of configuring the 7 Abrahamic religions by mapping them onto its 7 sides in contrasting clusters of 3 "Abrahamic" and 4 "Eastern" religions (as indicated above). If each religion were then to be associated with a particular style of fundamental question, this possibility would follow from a mapping of 7 such questions (Mapping of WH-questions with question-pairs onto the Szilassi polyhedron, 2014). The relatively simple form of that polyhedron suggests an appropriately complex insight into globality.
the globality sensed through the "magical" attraction of game-related interactivity, as variously exemplified across cultures (Sustainability through Magically Dancing Patterns: 8x8, 9x9, 19x19 -- I Ching, Tao Te Ching / T'ai Hsüan Ching, Wéiqí (Go), 2008).

The focus in this argument on the contrast between the static geometry of "plan" and "globe" reduces recognition of associated cognitive dynamics more evident in planning and integrating ("globalling"?). The latter could be fruitfully understood in terms of a "learning" process. The relation between plan and globe is then better recognized in the distinction made by Donald N. Michael (On Learning to Plan and Planning to Learn: the social psychology of changing toward future-responsive societal learning, 1973; Peter J. Brews, Learning to Plan and Planning to Learn: resolving the planning school/learning school debate. Strategic Management Journal, 1999).

Given the problematic implications of error with respect to any plan (and its ever-present "underside"), by use of the encompassing sense of "embrace" Michael effectively frames succinctly a valuable insight into a potentially fruitful relationship between plan-understanding and global-understanding. He argues:

On the requirement to embrace error: More bluntly, future-responsive societal learning makes it necessary for individuals and organizations to embrace error. It is the only way to ensure a shared self-consciousness about limited theory on the nature of social dynamics, about limited data for testing theory, and hence about our limited ability to control our situation well enough to be successful more often than not. (On Learning to Plan and Planning to Learn, 1973, p. 131).